Question

score: 2/3 penalty: none
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bao is trying to find the height of a radio antenna on the roof of a local building. she stands at a horizontal distance of 27 meters from the building. the angle of elevation from her eyes to the roof (point a) is 34°, and the angle of elevation from her eyes to the top of the antenna (point b) is 37°. if her eyes are 1.7 meters from the ground, find the height of the antenna (the distance from point a to point b). round your answer to the nearest tenth of a meter if necessary.
answer attempt 1 out of 2

Explanation:

Step1: Define variables for heights

Let $h_A$ = height from eyes to roof, $h_B$ = height from eyes to antenna top, $d = 27$ m (horizontal distance)

Step2: Calculate $h_A$ using tangent

$\tan(34^\circ) = \frac{h_A}{27}$
$h_A = 27 \times \tan(34^\circ) \approx 27 \times 0.6745 = 18.2115$ m

Step3: Calculate $h_B$ using tangent

$\tan(37^\circ) = \frac{h_B}{27}$
$h_B = 27 \times \tan(37^\circ) \approx 27 \times 0.7536 = 20.3472$ m

Step4: Find antenna height ($h_B - h_A$)

$\text{Antenna Height} = 20.3472 - 18.2115 = 2.1357 \approx 2.4$ m

Answer:

2.4 meters